Exploratory Factor Analysis of Data on a Sphere

TL;DR

This paper introduces a new factor analysis method for high-dimensional spherical data, enabling interpretable insights across diverse fields with efficient maximum likelihood estimation.

Contribution

It develops a novel exploratory factor analysis approach for projected normal distribution data on spheres, with a fast algorithm for maximum likelihood estimation.

Findings

Excellent performance in simulation studies.

Provides meaningful insights in real-world applications.

Efficient and interpretable factor analysis for spherical data.

Abstract

Data on high-dimensional spheres arise frequently in many disciplines either naturally or as a consequence of preliminary processing and can have intricate dependence structure that needs to be understood. We develop exploratory factor analysis of the projected normal distribution to explain the variability in such data using a few easily interpreted latent factors. Our methodology provides maximum likelihood estimates through a novel fast alternating expectation profile conditional maximization algorithm. Results on simulation experiments on a wide range of settings are uniformly excellent. Our methodology provides interpretable and insightful results when applied to tweets with the $\#MeToo$ hashtag in early December 2018, to time-course functional Magnetic Resonance Images of the average pre-teen brain at rest, to characterize handwritten digits, and to gene expression data from cancerous cells in the Cancer Genome Atlas.